Decoupling for certain quadratic surfaces of low co-dimensions

Abstract

We prove sharp ${\ell }^p{L}^p$ decoupling inequalities for $2$ quadratic forms in $4$ variables. We also recover several previous results (arXiv:1409.1634, arXiv:1501.07224, arXiv:1609.02022, arXiv:1609.04107) in a unified way.

v2: revised following referee reports, 22 pages

References in corpus (3)

• On the nonlinear Brascamp-Lieb inequality
• On integer solutions of Parsell-Vinogradov systems
• Decoupling for moment manifolds associated to Arkhipov--Chubarikov--Karatsuba systems

Cited by in corpus (3)

• Decoupling for two quadratic forms in three variables: a complete characterization
• Decoupling inequalities for quadratic forms
• Fourier decay of fractal measures on surfaces of co-dimension two in ${\mathbb{R}}^5$